Related papers: Novel Approximation of the Modified Mild Slope Equ…

We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…

We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…

A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…

The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…

Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…

In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…

This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…

An initial value problem of the one-dimensional nonlinear Schr\"odinger (NLS) equation with constant dispersive and nonlinear coefficients can be solved using a compact finite difference scheme (Xie, Li, & Yi, 2009). A similar scheme is…

An alternative way for the derivation of the new KdV-type equation is presented. The equation contains terms depending on the bottom topography (there are six new terms in all, three of which are caused by the unevenness of the bottom). It…

We propose a locally adaptive non-hydrostatic model and apply it to wave propagation generated by a moving bottom. This model is based on the non-hydrostatic extension of the shallow water equations (SWE) with a quadratic pressure relation,…

We consider a model equation from [14] that captures important properties of the water wave equation. We give a new proof of the fact that wave packet solutions of this equation are approximated by the nonlinear Schrodinger equation. This…

Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water…

We modify the nonlinear shallow water equations, the Korteweg-de Vries equation, and the Whitham equation, to permit constant vorticity, and examine wave breaking, or the lack thereof. By wave breaking, we mean that the solution remains…

This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived…

In the last decade, the perfectly matched layer (PML) approach has proved a flexible and accurate method for the simulation of waves in unbounded media. Most PML formulations, however, usually require wave equations stated in their standard…

Acoustic scattering from layered seafloors exhibits dependence on both the mean geoacoustic layering, as well as the roughness properties of each layer. Several theoretical treatments of this environment exist, including the small roughness…

Properties of modified plasma waves in non-linear electrodynamics are investigated. We consider a cold, uniform, collisionless, and magnetized plasma model. Initially, we also assume small amplitude waves and the non-relativistic…

We derive rigorously from the water waves equations new irrotational shallow water models for the propagation of surface waves in the case of uneven topography in horizontal dimensions one and two. The systems are made to capture the…

The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A recent development in computational fluid dynamics is to modify the linear transport equation…

This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…